Method and apparatus to mitigate multipath in rfid

ABSTRACT

A distance between at least one antenna of an interrogation system and a transponder, such as an RFID tag, is determined based on derivatives with respect to frequency of the phase and the signal strength of responses transmitted by the transponder and received at the at least one antenna. The derivatives of the phase and the signal strength facilitate compensating for sources of multipath interference. Determining changes in distance may further facilitate determining location, speed, or bearing of the transponder by the interrogation system.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims benefit under 37 U.S.C. 119(e) to U.S. patentapplication Ser. No. 61/432,091, filed Jan. 12, 2011, which isincorporated by reference herein in its entirety.

TECHNICAL FIELD

This disclosure generally relates to wireless transponders, for exampleradio frequency identification (RFID) transponders, and wirelessinterrogators, for example RFID interrogators or readers, andparticularly relates to multipath interference between the interrogatorsand the transponders.

BACKGROUND INFORMATION

Wireless radio or microwave frequency interrogators, for example radiofrequency identification (RFID) interrogators or readers, may be used toread information from and/or write information to transponders, forexample RFID transponders, commonly referred to as RFID tags.

RFID transponders or tags may store data in a wirelessly accessiblememory, and may include a discrete power source (i.e., an active RFIDtag), or may rely on power derived from an interrogation signal (i.e., apassive RFID tag). RFID readers typically emit a wireless interrogationor inquiry signal that causes the RFID transponder to respond with areturn wireless signal encoding the data stored in the memory. Thewireless signals typically have wavelengths falling in the radio ormicrowave portions of the electromagnetic spectrum. Whether radio ormicrowave frequencies are employed, such signals are commonly referredto as RF signals. Such a convention is adopted herein and throughout theattached claims.

Identification of an RFID transponder or tag generally depends on RFenergy produced by a reader or interrogator arriving at the RFIDtransponder and returning to the reader. Multiple protocols exist foruse with RFID transponders. These protocols may specify, among otherthings, particular frequency ranges, frequency channels, modulationschemes, security schemes, and/or data formats.

RFID transponders typically include a semiconductor device (e.g., achip) and one or more conductive traces that form an antenna. Thesemiconductor device includes an integrated circuit that typicallyincludes memory, logic circuitry and power circuitry. Typically, RFIDtransponders provide information stored in the memory in response to theRF interrogation signal received at the antenna from the interrogator orreader. Some RFID transponders include security measures, such aspasswords and/or encryption. Many RFID transponders also permitinformation to be written or stored in the memory via an RF signal.

While RFID transponders provide various types of information stored inmemory, the RFID transponders are presently incapable of transmittingtheir own coordinates of location to interrogators. Instead, techniquessuch as time difference of arrival (“TDOA”), time domain phase delay onarrival (“TD-PDOA”), spatial domain phase delay on arrival (“SD-PDOA”),and frequency domain phase delay on arrival (“FD-PDOA”) are used tocalculate the distance between an interrogator and an RFID transponder.However, such techniques have to date typically been unsuccessful inmultipath propagation environments. Multipath refers to reflections of awireless signal that result in reception of the wireless signal at anantenna via two or more paths. Outdoor sources of multipath include theground, the atmosphere, mountains and buildings, while indoor sources ofmultipath include floors, walls, ceilings, and metal objects. Sources ofmultipath introduce error in RFID transponder detection by affectingpower and phase measurements, thereby distorting information that may beextracted from the RF signals by interrogators.

Conventional understanding is that each of these techniques is incapableof producing accurate distance measurements, at least in the unlicensedISM (industrial, scientific and medical) band of 902-928 MHz commonlyused by UHF RFID, while compensating for the effects of practicalmultipath interference.

For example, TDOA requires operating RFID interrogators and transpondersin short pulse mode. UHF RFID is a very short range narrowbandtechnology, with a typical transponder read range on the order of 10-20feet. However, because the roundtrip signal delay for a range of 10-20feet is on the order of a few tens of nanoseconds and the bandwidth isnarrow, RFID interrogators and transponders cannot operate in the shortpulse mode required by TDOA.

As another example, distance measurements made using phase-basedtechniques according to conventional approaches, such as with TD-PDOA,SD-PDOA, and FD-PDOA, are prone to significant error in multipathenvironments. Multipath interference causes multiple rays of atransmitted RFID signal to constructively and destructively interferewith the signal strength and the phase of the transmitted RFID signal.Accordingly, RFID interrogators attempting to measure distance byemploying phase-based techniques in an indoor multipath environment mayresult in distance measurements with an error in excess of 300%.

New approaches for operating interrogators in multipath environments aredesirable.

BRIEF SUMMARY

In contrast to conventional approaches for determining distance betweenan interrogator and a transponder, frequency domain phase delay onarrival (“FD-PDOA”) may be used in conjunction with error correctiontechniques to accurately determine transponder distance, speed, andbearing with respect to an interrogator. In contrast to conventionalapproaches for operating a transponder, which disregard derivatives ofphase and signal strength of a response from an RFID transponder, thetechniques taught herein compensate for range errors due to multipath byutilizing derivatives of phase and signal strength.

Described herein are approaches that allow determination of the distancebetween an interrogator and a transponder. Such may be useful on itsown. Also described herein are approaches that allow determination ofspeed and/or bearing of a transponder relative to the interrogator orantenna(s) without a priori knowledge of the relative locations ofmultiple transponders.

An interrogation system to wirelessly interrogate wireless transpondersmay be summarized as including at least one antenna; a transmittercommunicatively coupled to the at least one antenna and operable totransmit interrogation signals at each of a plurality of frequencies ina wireless communications frequency band; a receiver communicativelycoupled to the at least one antenna to receive responses to theinterrogation signals; and a controller communicatively coupled with thetransmitter and the receiver and configured to: determine a first and asecond derivative of signal strength of the received responses withrespect to frequency over at least two of the frequencies, determine afirst and a second derivative of phase of the received responses withrespect to frequency over at least two of the frequencies, and determineat least one of a distance between the at least one antenna and awireless transponder that responds to the interrogation signals, abearing of the wireless transponder with respect to the at least oneantenna or a speed based at least in part on the determined first andthe determined second derivatives of signal strength of the receivedresponses with respect to frequency and the determined first and thedetermined second derivatives of phase of the received responses withrespect to frequency.

There may be only a single antenna and the transmitter and the receivermay be both communicatively coupled to the single antenna. The receivermay include a filter that filters out a direct current component of eachof the received responses. The filtered direct current component mayinclude a reader transmit-receive leakage. The controller may beconfigured to use an alternating current component from each response todetermine an in-phase component and a quadrature component, and thefirst and the second derivative of phase may be based on a differencebetween the quadrature components of at least two responses divided bythe in-phase components of the at least two responses. The controllermay be further configured to determine a distance of at least the atleast one antenna from at least one source of multipath. The controllermay compensate for the at least one source of multipath by determining adifference between a direct distance from the at least one antenna tothe transponder and an indirect distance from the at least one antennato the transponder, the indirect distance including a distance from theat least one antenna to the at least one source of multipath and adistance from the at least one source of multipath to the transponder.

The controller may be configured to determine an error in the distancedetermination between the at least one antenna and the wirelesstransponder according to:

$\overset{¨}{\phi} = {{- 2}A\; \Delta \; d^{2}\frac{\sin \; k\; \Delta \; d}{\left( {1 - {2\; A\; \cos \; k\; \Delta \; d} + A^{2}} \right)^{2}}\left( {1 - A^{2}} \right)}$and$\overset{.}{\frac{P}{P}} = \frac{{- 2}\; A\; \Delta \; d\; \sin \; k\; \Delta \; d}{1 - {2\; A\; \cos \; k\; \Delta \; d} + A^{2}}$

when a plot of signal strength verses frequency for responses isapproximately linear, wherein P is signal strength, A is a relativemagnitude of a reflected interrogation signal, and kΔd is a phase term.

A plot of signal strength verses frequency for responses may beapproximately linear when the phase term kΔd is M*Pi/2, wherein M is anodd integer.

The controller may be configured to determine the distance between theat least one antenna and the wireless transponder according to:

$\overset{¨}{\phi} \approx {{- 2}A\; \Delta \; d^{2}\frac{\left( {1 - A^{2}} \right)}{\left( {1 - A} \right)^{4}}\mspace{14mu} {and}\mspace{14mu} \overset{.}{\frac{P}{P}}} \approx \frac{{- 2}\; A\; \Delta \; d}{\left( {1 - A} \right)^{2}}$

when the phase term is Pi/2+2*Pi*M, wherein M is an integer, P is signalstrength, and A is a relative magnitude of a reflected interrogationsignal.

The interrogation system may further include a plurality ofinterrogators, wherein each of the plurality of interrogators isconfigured to communicate with each other interrogator of the pluralityof interrogators and the plurality of interrogators is configured todetermine the bearing or the speed of the transponder.

Communication between interrogators may include a first interrogator ofthe plurality of interrogators responding to a query made by a secondinterrogator of the plurality of interrogators as if the firstinterrogator were a second transponder.

The interrogation system may include a single interrogator, wherein theat least one antenna is a plurality of antennas.

A method of operating an interrogation system may be summarized asincluding transmitting interrogation signals from at least one antennaat each of a plurality of frequencies in a wireless communicationsfrequency band; receiving responses to the interrogation signals at theat least one antenna; determining a first and a second derivative ofsignal strength of the received responses with respect to frequency overat least two of the frequencies by a control subsystem; determining afirst and a second derivative of phase of the received responses withrespect to frequency over at least two of the frequencies by the controlsubsystem; and determining by the control subsystem at least one of adistance between the at least one antenna and a wireless transponderthat responds to the interrogation signals, a bearing of the wirelesstransponder with respect to the at least one antenna or a speed based atleast in part on the determined first and the determined secondderivatives of signal strength of the received responses with respect tofrequency and the determined first and the determined second derivativesof phase of the received responses with respect to frequency

The method of operating an interrogation system may further includefiltering a direct current component from each of the received responseand determining an in-phase component and a quadrature component of analternating current component of each received response, whereindetermining the first and second derivatives of phase includes based atleast in part on the in-phase component and the quadrature component.

The method of operating an interrogation system may further includedetermining by the control subsystem whether a maximum signal strengthand a minimum signal strength is measurable within the plurality offrequencies and determining a relative magnitude of a reflectedinterrogation signal reflected by a source of multipath interference ifthe maximum and the minimum is measurable.

Determining the first and the second derivative of phase of the receivedresponses with respect to frequency may include determining a differencebetween a direct distance from the antenna to the transponder and anindirect distance from the antenna to the transponder via a source ofmultipath interference.

Determining the difference between the direct distance and the indirectdistance may be performed according to:

$\overset{¨}{\phi} = {{- 2}A\; \Delta \; d^{2}\frac{\sin \; k\; \Delta \; d}{\left( {1 - {2\; A\; \cos \; k\; \Delta \; d} + A^{2}} \right)^{2}}\left( {1 - A^{2}} \right)}$and$\overset{.}{\frac{P}{P}} = \frac{{- 2}\; A\; \Delta \; d\; \sin \; k\; \Delta \; d}{1 - {2\; A\; \cos \; k\; \Delta \; d} + A^{2}}$

when a plot of signal strength verses frequency for responses isapproximately linear, wherein P is signal strength, A is a relativemagnitude of a reflected interrogation signal reflected by the source ofmultipath interference, and kΔd is a phase term.

Determining the difference between the direct distance and the indirectdistance may be performed according to:

$\overset{¨}{\phi} \approx {{- 2}A\; \Delta \; d^{2}\frac{\left( {1 - A^{2}} \right)}{\left( {1 - A} \right)^{4}}\mspace{14mu} {and}\mspace{14mu} \overset{.}{\frac{P}{P}}} \approx \frac{{- 2}\; A\; \Delta \; d}{\left( {1 - A} \right)^{2}}$

when a phase term is Pi/2+2*Pi*M, wherein M is an integer, P is signalstrength, and A is a relative magnitude of a reflected interrogationsignal.

The method of operating an interrogation system may further includedetermining by the control subsystem at least one of the frequencieswhere a phase term kΔd is one of 0+2*Pi*M, Pi/2+2*Pi*M, Pi+2*Pi*M, or3*Pi/2+2*Pi*M, wherein M is an integer, k=2*Pi/c, and Δd is differencebetween the distance between the at least one antenna and the wirelesstransponder and an indirect distance between the at least one antennaand the wireless transponder which includes a source of multipathinterference.

The method of operating an interrogation system may further includedetermining by the control subsystem at least two of the following atthe at least one of the frequencies where the phase term is one of0+2*Pi*M, Pi/2+2*Pi*M, Pi+2*Pi*M, or 3*Pi/2+2*Pi*M: the secondderivative of phase, a third derivative of phase, a first derivative ofsignal strength divided by signal strength, and a second derivative ofsignal strength divided by a first derivative of signal strength.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

Non-limiting and non-exhaustive embodiments are described with referenceto the following drawings, wherein like reference numerals refer to likeparts throughout the various views unless otherwise specified. The sizesand relative positions of elements in the drawings are not necessarilydrawn to scale. For example, the shapes of various elements and anglesare not drawn to scale, and some of these elements are arbitrarilyenlarged and positioned to improve drawing legibility. Further, theparticular shapes of the elements as drawn, are not intended to conveyany information regarding the actual shape of the particular elements,and have been solely selected for ease of recognition in the drawings.

FIG. 1 is a schematic diagram of an interrogator or reader interrogatinga transponder in a field including multipath interference sources,according to one illustrated embodiment.

FIG. 2 is a low level flow diagram of a method of operating aninterrogator or reader similar to that of FIG. 1, according to oneillustrated embodiment.

FIG. 3 is an in-phase verses quadrature phasor diagram of voltageresponses from a query of a transponder, according to an embodiment.

FIG. 4 is a graph of in-phase versus quadrature voltages of responsesreceived from multiple queries of a transponder.

FIG. 5 is a schematic diagram of a plurality of interrogators or readersinterrogating a transponder.

FIG. 6 is a high level flow diagram showing a method of operating aninterrogation system including a plurality of interrogators or readerssimilar to that of FIG. 6, according to one illustrated embodiment.

FIG. 7 is a diagram of a plurality of interrogators or readersperforming reader-to-reader communication, according to one illustratedembodiment.

FIG. 8 is a high level flow diagram showing a method of operating aplurality of interrogators or readers similar to that of FIG. 7, withouta priori knowledge of each interrogators' location, according to oneillustrated embodiment.

FIG. 9 is a schematic diagram of an interrogator or reader interrogatinga transponder through a plurality of antennas, according to oneillustrated embodiment.

DETAILED DESCRIPTION

In the following description, numerous specific details are given toprovide a thorough understanding of embodiments. The embodiments can bepracticed without one or more of the specific details, or with othermethods, components, materials, etc. In other instances, well-knownstructures, materials, or operations associated with transponders, forexample RFID transponders or tags, and interrogators or readers, forexample RFID readers, computer and/or telecommunications networks,and/or computing systems are not shown or described in detail to avoidobscuring aspects of the embodiments.

Unless the context requires otherwise, throughout the specification andclaims which follow, the word “comprise” and variations thereof, suchas, “comprises” and “comprising” are to be construed in an open,inclusive sense, that is as “including, but not limited to.”

Reference throughout this specification to “one embodiment” or “anembodiment” means that a particular feature, structure, orcharacteristic described in connection with the embodiment is includedin at least one embodiment. Thus, the appearances of the phrases “in oneembodiment” or “in an embodiment” in various places throughout thisspecification are not necessarily all referring to the same embodiment.Furthermore, the particular features, structures, or characteristics maybe combined in any suitable manner in one or more embodiments.

Reference throughout this specification and claims to “radio frequency”or RF includes wireless transmission of electromagnetic energy,including, but not limited to, energy with frequencies or wavelengthstypically classed as falling in the radio and microwave portions of theelectromagnetic spectrum.

The headings provided herein are for convenience only and do notinterpret the scope or meaning of the embodiments.

FIG. 1 shows an interrogator or reader 100 and a transponder 102 locatedwithin a range or field 104 of the interrogator or reader 100, accordingto one illustrated embodiment.

The range or field 104 includes one or more sources of multipathinference, denominated herein as reflectors 103 a-103 f (collectively103). While only one transponder 102 is illustrated, in typicalapplications there may be many more transponders 102 in the field 104.Similarly, while six reflectors 103 are illustrated, the field 104 maycontain any number of reflectors 103, even no reflectors. The numberand/or location or positions of the reflectors 103 may not be known apriori. The interrogator or reader 100 is operable to wirelesslytransmit a signal to the transponder 102, but does not have an a prioriknowledge of the distance or location of transponder 102 in the field104.

For simplicity of explanation hereinafter, the interrogator or reader100 will be described in the context of being an RFID reader that isdedicated to wirelessly reading RFID transponders. The terms reader andinterrogator are used interchangeably herein and in the claims to referto a device or system that is capable of transmitting an interrogationsignal into a field 103, and receiving a response signal from one ormore transponders 102 in the field. Typically, the reader orinterrogator 100 will receive a response signal encoding someinformation, for example a unique identifier. Some readers orinterrogators are capable of receiving other information fromtransponders, and/or writing information to transponders. Likewise, theterms range and field are used interchangeably herein and in the claims.The terms interrogation and inquiry are used interchangeably herein andin the claims to refer to a wireless signal transmitted or sent by aninterrogator or reader. Similarly, the terms response or return are usedinterchangeably herein and in the claims to refer to a wireless signaltransmitted or sent by a transponder or tag, for instance backscatteredthereby. The terms radio frequency or RF are used herein and in theclaims in their conventional sense, that is as encompassing that portionof the electromagnetic spectrum typically delineated as radio andmicrowave portions. Further, the terms signal and signals encompasstransmissions which may, or may not, include or encode data orinformation and/or instructions or commands. For instance, a signalincludes a transmission that does not encode data or instructions, butwhich simply provides power to a passive transponder. Also for instance,a signal includes transmissions that have collided such that informationencoded therein has become distorted or can no longer be recovered. Onlysignificant components of the reader 100 are illustrated, and lessrelevant components are not shown or described in detail in the interestof clarity of presentation.

While described in terms of RFID applications, the reader 100 andtransponders 102 can take various other forms. For example, the readeror interrogator 100 may only determine range and/or bearing of atransponder 102, without receiving an additionally information.Additionally, the reader 100 may be mobile, may be hand held, or may bea stationary (non-portable) or semi-stationary device (such as attachedto a forklift). Even further, the reader 100 can be a multi-mode devicehaving the capability to read other types of data carriers (e.g.,machine-readable symbols, touch memories, optical memories, magneticstripes, etc.) in addition to reading wireless transponders.

The reader 100 includes at least one antenna 106, a transmitter 108, areceiver 110, a housing 112, a carrier signal generator 114 and acontroller 116. The reader 100 wirelessly sends or transmits one or moreRF interrogation or inquiry signals 118 to one or more of thetransponders 102, and wirelessly receives one or more RF response orreturn signals 120 (only one called out in FIG. 1) sent by the RFIDtransponder(s) 102.

The inquiry signals 118 and the return signals 120 may pass between thereader 100 and the transponder 102 via multiple paths. Any reflectors103 in the field 104 and may cause reflections of the inquiry signals118 and reflections of the return signals 120 to be received inconjunction with the original signals at the reader 100 and thetransponder 102. The reflectors 103 may be indoor sources of multipathinterference such as may be commonly found within a warehouse, e.g., afloor, walls, a ceiling, a fork-lift or other large mechanicalequipment, machinery, vehicles, containers, or the like.

While multiple reflectors 103 may exist in the field 104, the reflector103 c closest to the direct path between the reader 100 and thetransponder 102 will typically be the largest source of multipathinterference, substantially greater than the interference produced bythe other reflectors 103 a, 103 b, 103 d, 103 e, and 103 f. This effectcan be attributed to path loss in propagation channels. Path lossbetween two communicating antennas may depend strongly on thepropagation environment. Path loss in free space is usually proportionalto d⁻², where d is the length of the ray path. However, at longdistances, e.g., distances including a reflection path, path loss isproportional to d⁻⁴. Consequently, the non-closest reflectors 103 a, 103b, 103 d, 103 e, and 103 f diminish exponentially by d⁻⁴ so that thenon-closest reflectors 103 a, 103 b, 103 d, 103 e, and 103 f may have anegligible effect in comparison to the closest reflector 103 c.

As illustrated, the reader 100 may include a single antenna 106 to bothtransmit the interrogation signals 118 and to receive the return signals120. The reader 100 may include a circulator 122 or similar element tocommunicatively couple the single antenna 106 to the transmitter 108 andreceiver 110. Alternatively, the reader 100 may include one or moreantennas for transmission and one or more separate antennas forreception. The antenna(s) 106 may be external or internal to the housing112. For the sake of simplicity of explanation, the reader 100 will bedescribed having the single antenna 106 used for both transmission andreception.

The transmitter 108 and the receiver 110 may each receive a signalgenerated by one or more carrier signal generators 114, for example viaa splitter 124. The carrier signal generator 114 may take a variety offorms. For example, the carrier signal generator 114 may take the formof a voltage controlled oscillator or local oscillator (LO) or similarcircuit or structure that generates a signal with a frequency of, orapproximate to, a frequency of the carrier wave. The carrier signalgenerator 114 may generate signals at frequencies suitable for theparticular transponders 102 and/or at a variety of frequencies toaccommodate various different types of transponders. The splitter 124 orsimilar circuit or structure splits the signal from the carrier signalgenerator between the transmitter 108 and receiver 110. Alternatively,the transmitter 108 and receiver 110 may receive signals from respectivecarrier signal generators or local oscillators, for example where theresponse signals 120 are on a carrier having a substantially differentfrequency than the carrier of the interrogation signals 118. Asillustrated, the controller 116 may be communicatively coupled tocontrol the carrier signal generator 114.

The transmitter 108 can take any of a variety of forms suitable towirelessly transmit interrogation signals or inquiries to thetransponders 102. The transmitter 108 may transmit at frequenciessuitable for the particular transponders 102 and/or at a variety offrequencies to accommodate various transponders. Likewise, thetransmitter 108 may employ any variety of protocols, for example Class 0or Class 1 Generation 1 protocols, or Class 1 Generation 2 protocol (ISO18000-6C). The controller 116 may be communicatively coupled to controlthe operation of the transmitter 108, and/or provide information or datato the transmitter 108 to be encoded into the interrogation signals 118.

The receiver 110 can take a variety of forms suitable to receivewireless response signals from transponders 102. The receiver 110 may beresponsive to frequencies suitable for the particular transponders 102and/or responsive to a variety of frequencies to accommodate varioustransponders. Likewise, the receiver 110 may be capable of handling anyvariety of protocols.

In particular, the receiver 110 demodulates the received signal intoin-phase and quadrature components. For example, one or more phaseshifters 126 (only one illustrated) may receive the signal generated bythe carrier signal generator 114, for example via the splitter 124. Thephase shifter 126 supplies an in-phase LO signal (i.e., I channel) to afirst mixer 128 a, and a quadrature LO signal (i.e., Q channel) to asecond mixer 128 b. The phase shifter 126 may take a variety of forms,for example a parallel combination of two varactors each respectivelycoupled in series with an inductor. The mixers 128 a, 128 b can take anyof a variety of forms suitable for down conversion of the received RFresponse signal using a local oscillator (LO) signal. Respective filters130 a, 130 b filter the in-phase I and quadrature Q analog basebandoutputs of the mixers 128 a, 128 b. The filters 130 a, 130 b may removeDC components of the demodulated signal, including readertransmit-receive leakage, static environment clutter, and backscatterfrom the transponder or tag (which contains both static and modulatedcomponents). Respective amplifiers 132 a, 132 b may baseband amplify thefiltered in-phase I and quadrature Q signals. Respectiveanalog-to-digital (ADC) converters or slicers 134 a, 134 b may sample,digitize or otherwise convert the in-phase I and quadrature Q analogbaseband outputs of the mixers 128 a, 128 b into a complex-valueddigital representation suitable for processing in the digital domain ofthe controller 116. While not illustrated, the receiver 118 may alsoinclude a comparator and other components for determining which of thein-phase I or quadrature Q components of the received response signal isstronger, and coupling that information to the controller 116.

The controller 116 may take a variety of forms and may include one ormore processors, for example one or more microprocessors 136, digitalsignal processors (DSPs) 138, application specific integrated circuits(ASICs) or programmable gate arrays (PGAs). The controller 116 may alsoinclude computer- or processor-readable storage media, for instance readonly memory (ROM) 140, random access memory (RAM) 142, flash memory 144,and/or other type of memory. The microprocessors 136, DSPs 138, ASICs,PGAs, ROM 140, RAM 142, and/or Flash memory 144 may be communicativelycoupled by one or more buses (not illustrated), for instance one or morepower busses, instruction busses, or data busses. The ROM 140, RAM 142,and/or Flash memory 144 may store instructions such as a computerprogram in the form of software or firmware. The instructions areexecutable by the microprocessors 136 and/or DSPs 138 to perform thevarious operations described herein pertaining to determining distancebetween the reader 100 and the transponder 102.

The controller 116 processes the digitized return signals 120 receivedby the reader 100, as well as to control the operation of various othercomponents (e.g., transmitter) of the reader 100 in response. Asexplained below, the controller 116 may control the transmission ofinterrogation signals 118 to determine derivatives of phases and signalstrengths of the received response signals 120 to determine thedistance, speed, and/or bearing of the transponder 102 in the field 104.

While not illustrated, the reader 100 may include a user interface whichmay include one or more user selectable or operable controls. Forexample, the reader may include one or more displays (e.g., liquidcrystal display (LCD)) upon which elements of a graphical or commandline user interface may be presented by the microprocessor 136. Also forexample, the user interface may include one or more actuators, forinstance one or more triggers, buttons, switches, keys, joystick,thumbstick, trackpad, touch screen, microphone, via which a user mayenter instructions, commands, data or information. Also for example, theuser interface may include one or more indicators, for instance one ormore optical indicators (e.g., light emitting diodes (LEDs, OLEDs)),speakers, and/or mechanical or tactile vibrators.

Also while not illustrated, the reader 100 may include other components122 to support operation thereof. Such components can include, forexample, communication components (e.g., wired port or connector forinstance USB ports, radio, cellular, WIFI and/or BLUETOOTH® chipsets) toenable the reader 100 to communicate with an external network/system(such as to download/upload data, information, instructions, commandsand/or software or firmware updates). Such components can include, forexample, a decryption chipset to decrypt encrypted information decodedfrom the received return signals 120. Such components can furtherinclude, for example, scanning and/or imaging components, for example ifthe reader 102 is a multi-mode automatic data collection device (e.g.,RFID and machine-readable symbol reader).

Also, while not illustrated the reader 100 may include one or more powersupplies and/or power sources. Power sources may, for instance, includeone or more batteries (e.g., primary or secondary), super- orultra-capacitor arrays, and/or fuel cells. Power supplies may, forinstance, include one or more rectifiers, inverters, DC/DC converters,and/or transformers. Power supplies may also, for instance, include atrickle charger circuit coupled to recharge a secondary battery from anexternal power source, such as from common AC power (e.g., 120V 60 Hz)via an AC power plug.

FIG. 2 shows a method 200 of operating a reader, for example the reader100, in the multipath environment illustrated in FIG. 1, according toone illustrated embodiment. The method 200 of operating the reader mayperform frequency domain phase difference of arrival (“FD-PDOA”)estimation.

As an overview of the method 200, the reader transmits an interrogationor inquiry signal at a frequency and receives a response from atransponder. The reader repeats this procedure, varying the frequencyuntil the transponder is queried at a plurality of frequencies and acorresponding plurality of responses is received. The reader thendetermines the phase of each response as well as first, second, andthird derivatives of the phase. The reader also determines the signalstrength and power of each response as well as first, second, and thirdderivatives of the power.

At 202, the reader sets a counter i that the reader may use toiteratively query a transponder at a plurality of frequencies. Inparticular, the controller may set the counter i to 0 to begin countingthrough a sequence of frequencies.

At 204, the reader transmits a query with an array of basebandfrequencies f_(i). The array of baseband frequencies f_(i) for the queryis accessed as the counter i changes. The array of baseband frequenciesf_(i) may be a range of frequencies spanning a particular portion of theRF spectrum. In particular, the range of frequencies may span theunlicensed ISM (industrial, scientific and medical) band of 902-928 MHzused by UHF RFID.

Each frequency element in the array may be set manually, for example, bya user. Alternatively, each frequency or element in the array may bedetermined by establishing a range of frequencies over which querieswill be transmitted and by setting the size of the array. Each increasein frequency in the array may be uniform throughout the array.Alternatively, some increases in frequency between array elements mayvary in accordance with a function, in accordance with a user-enteredpreference, or randomly.

At 206, the reader receives a response to the query from a transponderin the field. The response from a passive transponder may be modulated,so as to distinguish the response from that of a mere reflection. Atransponder may modulate its response or backscattered signal byswitching its input impedance between two states (e.g., a high impedancestate and a low impedance state). At each impedance state, thetransponder projects a specific power. A difference in power levelsbetween each impedance state may be used to determine a phase of theresponse.

At 208, the counter i may be incremented in order to access a subsequentfrequency in the array of baseband frequencies f_(i). The counter i andquery transmissions may be managed by the transmitter. Alternatively,the controller or carrier signal generator may manage counter i andquery transmissions.

At 210, the reader may compare the counter i with a number of queries n.If the counter i is not equal to the number of queries n, the reader mayhave another query transmitted. If the counter i is equal to the numberof queries n, control may pass to 212.

Before the signal strength and phase of the responses are determined,the reader demodulates the received responses. In particular, thereceiver may down convert the received responses into alternatingcurrent (“AC”) in-phase and quadrature components. This may includeemploying phase shifters, mixers, and filters. For example, some of thedirect current (“DC”) parts of the response that may be removed includethe reader transmit-receive leakage. Isolation between transmit andreceive channels facilitates proper detection and decoding oftransponder responses. Other DC parts of the response that may befiltered out include static environment clutter and backscatter from thetransponder or tag. The remaining AC in-phase and quadrature componentsof the responses may be utilized to determine the signal strength andphase of the received responses.

At 212, the reader determines the phase φ of each transponder responseaccording to the queries transmitted at each frequency in the basebandfrequency array f_(i). The reader may determine the phase φ based on theAC in-phase and component I_(ac) and the AC quadrature component Q_(ac)of each response. This may more easily be understood in view of a phasordiagram and IQ plot.

FIG. 3 is a phasor diagram illustrating state 1 and state 2 of amodulated backscatter response received at the reader from of atransponder, according to one illustrated embodiment.

The complex demodulated voltage at the reader can be written as the sumof three components:

{right arrow over (V)}={right arrow over (V)} _(leakage) +{right arrowover (V)} _(clutter) +{right arrow over (V)} _(tag),

where {right arrow over (V)}_(leakage) is the voltage due to the readertransmit-receive leakage (including reflection from the mismatchedreader antenna), {right arrow over (V)}_(clutter) is the voltage due tothe scatter from the static environment clutter, and {right arrow over(V)}_(tag) is the voltage due to the backscatter from the tag when thetag is in either state 1 or state 2.

FIG. 4 shows the AC in-phase component I_(ac) and quadrature componentQ_(ac) of FIG. 3 after the DC part of the signals has been filtered out.

After removal of the DC part of the signals, the constellation of thetransponder responses to queries of a single baseband frequency iscentered at zero and may be dumbbell-shaped.

The received phase φ may be determined by converting the in-phasecomponent I_(ac) and the quadrature component Q_(ac) from rectangularcoordinates to polar coordinates. Thus, the phase φ is:

$\phi = {{{ang}\left( {{\overset{\rightarrow}{V}\mspace{14mu} {tag}\mspace{14mu} {state}\mspace{14mu} 2} - {\overset{\rightarrow}{V}\mspace{14mu} {tag}\mspace{14mu} {state}\mspace{14mu} 1}} \right)} = {{\arctan \left( \frac{Q_{ac}}{I_{ac}} \right)}.}}$

Because the phase φ of a response may be measured, characterization ofand compensation for multipath interference may be accomplished usingexpressions or formulae which take advantage of a known value of thephase φ. For example, in a 2-ray environment, i.e., a direct ray and anindirect ray, the field incident on a transponder contains the followingterm:

S=1−Ae ^(−jkΔd)=1−A cos(kΔd)+jA sin(kΔd),

where 0<A<1 is the relative magnitude of a reflected ray, Δd is thedifference in paths between the direct and reflected rays, and k is thewave vector proportional to frequency and is expressed as:

${k = \frac{2\pi \; f}{c}},$

c being the speed of light. The phase φ, may then be expressed as:

${\phi = {F - {2\; {kG}} - {2{kd}} + {2{\arctan \left( \frac{A\; {\sin \left( {k\; \Delta \; d} \right)}}{1 - {A\; {\cos\left( {k\; \Delta \; d} \right.}}} \right)}}}},$

where F includes various constant phase offsets and G includestransmission line length in the reader, connecting cables, and antennaassembly.

Expressing the phase φ in the manner above exposes variables that, whensolved, provide the distance d between the reader and the transponderwhile compensating for influence of multipath interference.Additionally, the above expression provides information about a sourceof multipath interference that may be unknown a priori. In particular, Aindicates the relative magnitude of the reflected ray and Δd indicateshow much farther the reflected ray traveled to the transponder via thesource of multipath interference. Accordingly, solving for the unknownvariables d, A and Δd may determine the distance of the transponderrelative to the reader and facilitate characterizing and compensatingfor the source of multipath interference.

The reader may determine the signal strength and the phase of thereceived responses as they are received rather than after an array ofqueries has been transmitted. In particular, a controller may beoperable to cause the receiver or a processor to determine phase andsignal strength of the received responses as the responses are received.

At 214, the reader determines the derivative with respect to frequencyof the phase φ of the received responses. The derivative of the phase φmay be expressed as:

${\frac{\partial\phi}{\partial f} = {{{- 2}G} - {2d} + {\frac{\partial\phi}{{\partial f}\;}{error}_{\phi}}}},{and}$${\frac{\partial\phi}{\partial f}\mspace{14mu} {error}} = {{- 2}A\; \Delta \; d{\frac{A - {\cos \; k\; \Delta \; d}}{1 - {2A\; \cos \; k\; \Delta \; d} + A^{2}}.}}$

This expressions of the derivative of the phase φ may be used with theexpression for the phase φ to determine the distance d to thetransponder from the reader, A, and Δd.

In narrowband interrogation, the phase error introduced above may bedeterminative in whether or not a ranging technique such as FD-PDOAestimation can produce viable results. The additive nature of phasepresents challenges when attempts are made to distinguish the influenceof indirect rays from direct rays of queries. In many practical cases,significant variation of the phase term kΔd may be observed in the902-928 MHz band. For example, difference in paths (Δd) of 10 feetresults in transponder phase changing over that band by 95 degrees. Theinfluence of multipath interference on phase may result in errors indistance measurements exceeding 300%. That is, a transponder that isonly 1.4 meters away may be read as being more than 5.6 meters away.This is a significant amount of error when the typical transponder rangefrom the reader is 1.5-6.1 meters (5-20 feet).

The reader may determine the value of the derivative based on theresponses received by the receiver from the transponder using varioustechniques. For example, the reader may determine the difference betweenphase φ measurements and divide by the difference between thecorresponding baseband frequencies of the queries from which the phase φmeasurements originated. Alternatively, the reader may use complicatedalgorithms to determine the derivative.

At 216, the reader may determine the second derivative with respect tofrequency of the phase φ. The value of the second derivative may bedetermined based on measured values of the phase φ at variousfrequencies. As a result, the quality of the second derivative maydepend upon the number of samples acquired, i.e., the number of queriestransmitted. The expression of the second derivative of the phase φ interms of A and Δd may be combined with the expressions for the phase φand the derivative of the phase φ to determine the distance d to thetransponder and to determine the phase error injected into the signal bythe source of multipath interference.

At least two expressions may be used to represent the second derivativeof the phase φ. As will be described in more detail in connection steps220-226, a power P verses frequency curve may result in easilyattainable solutions of A. When the power P verses frequency curve lookslinear, i.e., kΔd is either π/2, or 3π/2, etc., an expression for thesecond derivative of the phase φ is:

$\frac{\partial^{2}\phi}{\partial f^{2}}\; = {{- 2}A\; \Delta \; d^{2}\frac{\sin \; k\; \Delta \; d}{\left( {1 - {2A\; \cos \; k\; \Delta \; d} + A^{2}} \right)^{2}}{\left( {1 - A^{2}} \right).}}$

A second expression for the second derivative of the phase φ occurs whenthe phase term kΔd is off by π from the first expression for the secondderivative. In particular, when the phase term kΔd is π/2+2π*M, where Mis an integer, the second derivative of the phase φ can be reduced to:

$\frac{\partial^{2}\phi}{\partial f^{2}} = {{- 2}A\; \Delta \; d^{2}{\frac{\left( {1 - A^{2}} \right)}{\left( {1 - A} \right)^{4}}.}}$

Thus, the three expressions of phase including the phase φ, thederivative of the phase φ, and the second derivative of the phase φ arethree equations that may be used to solve for the three unknowns, i.e.,d, A, and Δd.

At 218, the reader may determine the third derivative of the phase φ. Ina manner similar to the preceding, the value of the third derivative maybe obtained by exercising any one of a variety of techniques using themeasurements of phase with respect to frequency. Additionally, the thirdderivative may also be expressed in terms of Δd and A for at least thetwo cases described in connection with determining the second derivativewith respect to frequency of the phase φ 216. Taking the thirdderivative with respect to frequency of the phase φ may provide anadditional equation by which the unknown variables d, A, and Δd may besolved. The reader may solve multiple equations with multiple unknownsusing various techniques, including the linear algebraic technique ofsimultaneously solving the equations.

At 220, the reader determines a power P of each transponder response foreach frequency in the baseband frequency array f_(i). The power P isproportional to the square root of the signal strength RSSI. The readermay determine the signal strength RSSI based on the AC in-phasecomponent I_(ac) and the AC quadrature component Q_(ac) of eachresponse.

Referring again to FIG. 3, the received signal strength RSSI may bedetermined as approximately the square of the difference between state 1and state 2 of the transponder backscatter:

${{RSSI} = {{\frac{1}{2}\frac{{{{\overset{\rightarrow}{V}\mspace{14mu} {tag}\mspace{14mu} {state}\mspace{14mu} 2} - {\overset{\rightarrow}{V}\mspace{14mu} {tag}\mspace{14mu} {state}\mspace{14mu} 1}}}^{2}}{Z_{o}}} = \frac{I_{ac}^{2} + Q_{ac}^{2}}{Z_{o}}}},$

where Z_(o) is the input impedance of the reader, e.g. 50Ω. As a result,characterizations of multipath interference may be facilitated usingexpressions or formulae which take advantage of a known or measuredvalue of RSSI and the power P. With reference to the term within thefield incident on a transponder,

S=1−Ae ^(−jkΔd)=1−A cos(kΔd)+jA sin(kΔd),

the signal strength RSSI, which is proportional to |S|⁴, and power P,which is proportional to |S|², may then be expressed as:

P=√{square root over (RSSI)}=E(1−2A cos(kΔd)+A ²),

where E is a constant including reader receiver channel gains and freespace path loss. This expression of the power P may be combined withexpressions of the phase φ to determine the unknown variables A and Δd.

In some instances, the unknown variable A may be determined based solelyminimums and maximums of the power P. As can be seen from the aboveexpression for power, a minimum of the power P exists when the phaseterm kΔd is 0, 2π, or multiples thereof. A maximum of the power P existswhen the phase term kΔd is π, 3π, or other odd multiples of π. When thephase term kΔd is π/2, 3π/2, or other odd multiples of π/2, the power Pis at a mid-point.

The unknown variable A, i.e., the relative magnitude of a reflected ray,may be determined based on expressions of a maximum P_(max) of the powerP and a minimum P_(min) of the power P. A ratio of P_(max) to P_(min)may be expressed by:

$\frac{P_{\max}}{P_{\min}} = {\frac{\left( {1 + A} \right)^{2}}{\left( {1 - A} \right)^{2}}.}$

Accordingly, solving for the relative magnitude A, results in:

$A = {\frac{\sqrt{\frac{P_{\max}}{P_{\min}}} - 1}{\sqrt{\frac{P_{\max}}{P_{\min}}} + 1}.}$

If minima and maxima of the power P are not determinable within the bandof frequencies, e.g., 902-928 MHz, the reader may construct an N^(th)order polynomial approximation to the power P with respect to frequency.The reader may determine parabolic coefficients using an N number offrequencies to then estimate P_(max), P_(min), and the frequency atwhich the phase term kΔd is either π/2 or 3π/2.

At 222, the reader determines the derivative with respect to frequencyof the power P. The reader may execute any number of suitable algorithmsto determine the derivative with respect to frequency of the power P ofresponses received from a transponder by the reader. When the power Pverses frequency curve looks linear, i.e., kΔd is either π/2, or 3π/2,etc., an expression for the derivative of the power P may be:

$\frac{\partial P}{\partial f} = {{- 2}A\; \Delta \; d\; {{\sin \left( {k\; \Delta \; d} \right)}.}}$

Thus, the ratio of the derivative of the power P to the power P may beexpressed as:

$\overset{.}{\frac{P}{P}} = {\frac{{- 2}A\; \Delta \; d\; {\sin \left( {k\; \Delta \; d} \right)}}{1 - {2A\; \cos \; \left( {k\; \Delta \; d} \right)} + A^{2}}.}$

A second expression for the derivative of the power P occurs when thephase term kΔd is off by π from the first expression for the derivative.In particular, when the phase term kΔd is π/2+2π*M, where M is aninteger, the derivative of the power P can be reduced to:

$\frac{\partial P}{\partial f} = {{- 2}A\; \Delta \; {d.}}$

Thus, the ratio of the derivative of the power P to the power P may beexpressed as:

$\overset{.}{\frac{P}{P}} = {\frac{{- 2}A\; \Delta \; d}{\left( {1 - A}\; \right)^{2}\;}.}$

As discussed previously in connection with the various expressions forthe phase φ, the reader or interrogator may combine these expressions ofthe power P with the known or measured values of the power P tofacilitate the determination of the distance d, relative magnitude A,and difference in paths Δd.

FIG. 5 shows an interrogation system 500 including a plurality ofinterrogators or readers 506 a-506 c (collectively 506), and at leastone transponder 502 located within a range or field 504 of theinterrogators or readers 506, according to one illustrated embodiment.

The field 504 may include a number of reflectors 510 a-510 j(collectively 510). The reflectors represent various potential sourcesof multipath interference. The field 104 may contain any number ofreflectors 103, even no reflectors. While only three readers 506 areillustrated, an application may employ any number of readers 506. Thereaders 506 may be individually coupled to antennas 508 a-508 c(collectively 508) to transmit queries to the transponder 502 andreceive responses from the transponder 502. The interrogator or readers506 are operable to wirelessly transmit a signal to the transponder 102,but does not have an a priori knowledge of the distance or location oftransponder 102 in the field 104.

Because path loss at long distances is proportional to d⁻⁴, where d isthe length of the ray's path, the readers 506 may neglect reflectors 510that are not located closest to direct paths between readers 506 and thetransponder 502.

The interrogation system 500 may employ the techniques previouslydescribed in connection with method 200 to determine a distance betweeneach of the readers 506 and the transponder 502. The readers 506 mayhave a priori data indicating relative locations of the readers 506 withrespect to one another, or relative to some common or generalizedcoordinate system. Accordingly, the readers 506 may determine athree-dimensional location of the transponder 502 based on anintersection of the distances between each of the readers 506, e.g., viatriangulation.

FIG. 6 shows a method 600 of operating an interrogation system similaror identical to that of FIG. 5, according to one illustrated embodiment.

At 602, the interrogation system determines the relative locations ofeach of the readers in the interrogation system. The locations may beentered in manually, the locations may be determined via globalpositioning systems, the locations may be determined via wiresinterconnecting the readers, i.e., time domain reflectometry, or bytransmitting signals back and forth between readers while taking turnsacting as transponders or tags.

At 604, each reader in the interrogation system interrogates thetransponder with a plurality of queries over a plurality of frequencies.Alternatively, a single reader may transmit a plurality of queries onbehalf of all of the readers of the interrogation system. Each readermay transmit queries using baseband frequencies unique to each reader toassist each reader in distinguishing responses to queries transmitted byeach reader. Alternatively, each reader may encode a reader-uniqueidentifier in the transmitted queries, for example to temporarilysilence all but a desired one of the transponder from responding.

At 606, each reader receives transponder responses to the queriestransmitted by each reader in the interrogation system.

At 608, the interrogation system determines the relative distancebetween each reader and the transponder based on the phase and signalstrength of the received transponder responses. The distance may bedetermined using the technique described with respect to method 200.

At 610, the transponder system determines a three-dimensional locationof the transponder based on the distance between each reader and thetransponder. The three-dimensional location may be determined usingtechniques such as triangulation. The transponder system may use thethree-dimensional location of the transponder to determine the speed andthe bearing of the transponder.

FIG. 7 shows an interrogation system 700 including a plurality ofinterrogators or readers 706 a-706 c (collectively 706) and operable tointerrogate a transponder 702 in a range or field 704 of a plurality ofinterrogators or readers 706. The readers 706 may be individuallycoupled to respective antennas 708 a-708 c (collectively 708) totransmit queries and responses between the readers 706, as well as toand from transponder 702.

The field 704 may include one or more sources of multipath interference,denominated herein as reflectors 710 a-710 j (collectively 710). Thereflectors represent various potential sources of multipath interferencewhich may distort RF signals transmitted between readers 706. While tenreflectors 710 are illustrated, the field 704 may contain any number ofreflectors, even no reflectors. The number and/or location or positionsof the reflectors may not be known a priori. The readers 706 areoperable to wirelessly transmit signals to one or more transponders, butthe readers 706 typically will not have an a priori knowledge of thenumber and or location or position of the transponders.

Each reader 706 may transmit queries and responses between each otherreader 706 to determine the location of each reader 706 relative to eachother reader 706. The readers 706 may also transmit acquired informationregarding any transponders that may exist in the field 704.

FIG. 8 shows a method 800 of operating an interrogation system includingmultiple interrogators or readers similar to that illustrated in FIG. 7,according to one illustrated embodiment where the location of eachreader relative to each other reader may not be known a priori. Asdiscussed in more detail below, reader-to-reader communication may beused to determine the location of each reader relative to each otherreader. During the reader-to-reader communication, each reader may taketurns responding to each other reader as if the reader were atransponder or RFID tag.

At 802, each reader transmits queries to each other reader. Each readermay transmit queries to each other reader by modifying the techniquesdescribed in method 200 so that each queried reader responds as if itwere a transponder or RFID tag. The reader-to-reader query may include:an ID of the transmitting reader, a command, the date, the time, apriority level of the transmission, or the like. The information may bemodulated onto the baseband frequency using amplitude shift keying,binary shift keying, frequency shift keying, or the like. Alternatively,the reader-to-reader query may be transmitted in a manner that is tooweak to power up a transponder, thereby only enabling other readers torespond.

At 804, each reader transmits responses to queries received from eachother reader. For simplicity, each reader may respond to areader-to-reader query by entering transponder mode. In transpondermode, each reader may respond to a reader-to-reader query as if thereader were a transponder. In particular, each reader may respond to areader-to-reader query by modulating the response between a firstimpedance state and a second impedance state. Additionally, each readermay modulate the response to include: an ID of the responding reader,the date, the time, or other information to facilitate reader-to-readercommunication.

At 806, the interrogation system determines the relative location ofeach reader with respect to each other reader based on the determineddistance between each of the readers. The distances between each of thereaders may be determined based on the responses of each reader by usingthe techniques described in connection with method 200.

At 810, the interrogation system determines the distance between eachreader and a transponder in accordance with the technique described inmethod 200.

At 812, the transponder system determines a three-dimensional locationof the transponder based on the distance between each reader and thetransponder. The three-dimensional location may be determined usingtechniques such as triangulation. According to one embodiment, thetransponder system may use the three-dimensional location of thetransponder to determine the speed and the bearing of the transponder.

FIG. 9, shows an interrogation system 900 including an interrogator orreader 906 and operable to interrogate a transponder 902 in a range orfield 904 in which one or more reflectors 910 a-910 f (collectively 910)may exist. While only one transponder 902 is illustrated, in typicalapplications there may be many more transponders 902 in the field 904.Similarly, while only six reflectors 910 are illustrated, the field 904may contain any number of reflectors 910, even no reflectors. The numberand/or location or positions of the reflectors 910 may not be known apriori. The interrogator or reader 902 is operable to wirelesslytransmit a signal to the transponder 902, but does not have an a prioriknowledge of the distance or location of transponder 902 in the field904

The interrogator 906 may be connected to multiple antennas 908 a-908 c(collectively 908) positioned within the field 904. While three antennas908 are illustrated, more antennas 908 may be connected to theinterrogator 906. The antennas 908 may be equidistantly positionedaround the field 904 to improve coverage of the field 904 and to improveranging accuracy.

The locations of the antennas 908 may be not be known a priori. If thelocation of each antenna 908 is not known, the locations may bedetermined using the technique described in method 800.

The three-dimensional location of the transponder 902 may be determinedusing the techniques described above in connection with otherembodiments. Accordingly, the range, speed, and bearing of thetransponder 902 with respect to antennas 908 may be determined usinginterrogation system 900.

The various embodiments described above can be combined to providefurther embodiments. Aspects of the embodiments can be modified, toprovide yet further embodiments. For example, the techniques describedabove may also be applied to time domain phase difference of arrivalestimation and spatial domain phase difference of arrival estimation.

These and other changes can be made to the embodiments in light of theabove-detailed description. In general, in the following claims, theterms used should not be construed to limit the claims to the specificembodiments disclosed in the specification and the claims, but should beconstrued to include all possible embodiments along with the full scopeof equivalents to which such claims are entitled. Accordingly, theclaims are not limited by the disclosure.

1. An interrogation system to wirelessly interrogate wirelesstransponders, comprising: at least one antenna; a transmittercommunicatively coupled to the at least one antenna and operable totransmit interrogation signals at each of a plurality of frequencies ina wireless communications frequency band; a receiver communicativelycoupled to the at least one antenna to receive responses to theinterrogation signals; and a controller communicatively coupled with thetransmitter and the receiver and configured to: determine a first and asecond derivative of signal strength of the received responses withrespect to frequency over at least two of the frequencies, determine afirst and a second derivative of phase of the received responses withrespect to frequency over at least two of the frequencies, and determineat least one of a distance between the at least one antenna and awireless transponder that responds to the interrogation signals, abearing of the wireless transponder with respect to the at least oneantenna or a speed based at least in part on the determined first andthe determined second derivatives of signal strength of the receivedresponses with respect to frequency and the determined first and thedetermined second derivatives of phase of the received responses withrespect to frequency.
 2. The interrogation system of claim 1 whereinthere is only a single antenna and the transmitter and the receiver areboth communicatively coupled to the single antenna.
 3. The interrogationsystem of claim 1 wherein the controller is further configured todetermine a magnitude of the responses based on at least one of amaximum and a minimum signal strength of the received responses.
 4. Theinterrogation system of claim 3 wherein the controller is configured toestimate the at least one of the maximum and the minimum signal strengthof the received responses by construction of an Nth-order polynomialapproximation of a function of signal strength of the received responseswith respect to the plurality of frequencies.
 5. The interrogationsystem of claim 1 wherein the controller is configured to use analternating current component from each response to determine anin-phase component and a quadrature component, and the first and thesecond derivative of phase is based on a difference between thequadrature components of at least two responses divided by the in-phasecomponents of the at least two responses.
 6. The interrogation system ofclaim 1 wherein the controller is further configured to determine adistance of at least the at least one antenna from at least one sourceof multipath.
 7. The interrogation system of claim 6 wherein thecontroller compensates for the at least one source of multipath bydetermining a difference between a direct distance from the at least oneantenna to the transponder and an indirect distance from the at leastone antenna to the transponder, the indirect distance including adistance from the at least one antenna to the at least one source ofmultipath and a distance from the at least one source of multipath tothe transponder.
 8. The interrogation system of claim 1 wherein thecontroller is configured to determine an error in the distancedetermination between the at least one antenna and the wirelesstransponder according to:$\overset{¨}{\phi}\; = {{- 2}A\; \Delta \; d^{2}\frac{\sin \; k\; \Delta \; d}{\left( {1 - {2A\; \cos \; k\; \Delta \; d} + A^{2}} \right)^{2}}\left( {1 - A^{2}} \right)}$and${\overset{.}{\frac{P}{P}} = \frac{{- 2}A\; \Delta \; d\; \sin \; k\; \Delta \; d}{1 - {2A\; \cos \; k\; \Delta \; d} + A^{2}}},$wherein P is signal strength, A is a relative magnitude of a reflectedinterrogation signal, and kΔd is a phase term.
 9. The interrogationsystem of claim 8 wherein the controller is configured to account for atleast one source of multipath that is nearest a direct path between theat least one antenna and the wireless transponder and configured todisregard any other sources of multipath interference to compensate forthe error in the distance determination between the at least one antennaand the wireless transponder.
 10. The interrogation system of claim 1wherein the controller is configured to determine the distance betweenthe at least one antenna and the wireless transponder according to:$\overset{¨}{\phi} \approx {{- 2}A\; \Delta \; d^{2}\frac{\left( {1 - A^{2}} \right)}{\left( {1 - A} \right)^{4}}\mspace{14mu} {and}\mspace{14mu} \overset{.}{\frac{P}{P}}} \approx \frac{{- 2}A\; \Delta \; d}{\left( {1 - A}\; \right)^{2}\;}$when the phase term is Pi/2+2*Pi*M, wherein M is an integer, P is signalstrength, and A is a relative magnitude of a reflected interrogationsignal.
 11. The interrogation system of claim 1, comprising: a pluralityof interrogators, wherein each of the plurality of interrogators isconfigured to communicate with each other interrogator of the pluralityof interrogators and the plurality of interrogators is configured todetermine the bearing or the speed of the transponder.
 12. Theinterrogation system of claim 11 wherein communication betweeninterrogators includes a first interrogator of the plurality ofinterrogators responding to a query made by a second interrogator of theplurality of interrogators as if the first interrogator were a secondtransponder.
 13. The interrogation system of claim 1 wherein theinterrogation system includes a single interrogator, wherein the atleast one antenna is a plurality of antennas.
 14. A method of operatingan interrogation system, comprising: transmitting interrogation signalsfrom at least one antenna at each of a plurality of frequencies in awireless communications frequency band; receiving responses to theinterrogation signals at the at least one antenna; determining a firstand a second derivative of signal strength of the received responseswith respect to frequency over at least two of the frequencies by acontrol subsystem; determining a first and a second derivative of phaseof the received responses with respect to frequency over at least two ofthe frequencies by the control subsystem; and determining by the controlsubsystem at least one of a distance between the at least one antennaand a wireless transponder that responds to the interrogation signals, abearing of the wireless transponder with respect to the at least oneantenna or a speed based at least in part on the determined first andthe determined second derivatives of signal strength of the receivedresponses with respect to frequency and the determined first and thedetermined second derivatives of phase of the received responses withrespect to frequency
 15. The method of claim 14, further comprising:filtering a direct current component from each of the received responseand determining an in-phase component and a quadrature component of analternating current component of each received response, whereindetermining the first and second derivatives of phase includes based atleast in part on the in-phase component and the quadrature component.16. The method of claim 14, further comprising: determining by thecontrol subsystem whether a maximum signal strength and a minimum signalstrength is measurable within the plurality of frequencies anddetermining a relative magnitude of a reflected interrogation signalreflected by a source of multipath interference if the maximum and theminimum is measurable.
 17. The method of claim 14 wherein determiningthe first and the second derivative of phase of the received responseswith respect to frequency includes determining a difference between adirect distance from the antenna to the transponder and an indirectdistance from the antenna to the transponder via a source of multipathinterference.
 18. The method of claim 17 wherein determining thedifference between the direct distance and the indirect distance isperformed according to:$\overset{¨}{\phi}\; = {{- 2}A\; \Delta \; d^{2}\frac{\sin \; k\; \Delta \; d}{\left( {1 - {2A\; \cos \; k\; \Delta \; d} + A^{2}} \right)^{2}}\left( {1 - A^{2}} \right)}$and${\overset{.}{\frac{P}{P}} = \frac{{- 2}A\; \Delta \; d\; \sin \; k\; \Delta \; d}{1 - {2A\; \cos \; k\; \Delta \; d} + A^{2}}},$wherein P is signal strength, A is a relative magnitude of a reflectedinterrogation signal reflected by the source of multipath interference,and kΔd is a phase term.
 19. The method of claim 17 wherein determiningthe difference between the direct distance and the indirect distance isperformed according to:$\overset{¨}{\phi} \approx {{- 2}A\; \Delta \; d^{2}\frac{\left( {1 - A^{2}} \right)}{\left( {1 - A} \right)^{4}}\mspace{14mu} {and}\mspace{14mu} \overset{.}{\frac{P}{P}}} \approx \frac{{- 2}A\; \Delta \; d}{\left( {1 - A}\; \right)^{2}\;}$when a phase term is Pi/2+2*Pi*M, wherein M is an integer, P is signalstrength, and A is a relative magnitude of a reflected interrogationsignal.
 20. The method of claim 14, further comprising: determining bythe control subsystem at least one of the frequencies where a phase termkΔd is one of 0+2*Pi*M, Pi/2+2*Pi*M, Pi+2*Pi*M, or 3*Pi/2+2*Pi*M,wherein M is an integer, k=2*Pi/c, and Δd is difference between thedistance between the at least one antenna and the wireless transponderand an indirect distance between the at least one antenna and thewireless transponder which includes a source of multipath interference.21. The method of claim 19, further comprising: determining by thecontrol subsystem at least two of the following at the at least one ofthe frequencies where the phase term is one of 0+2*Pi*M, Pi/2+2*Pi*M,Pi+2*Pi*M, or 3*Pi/2+2*Pi*M: the second derivative of phase, a thirdderivative of phase, a first derivative of signal strength divided bysignal strength, and a second derivative of signal strength divided by afirst derivative of signal strength.